Leonid Bunimovich
Georgia Tech
Chaotic dynamics is generated by an intrinsic instability of a system's evolution. We will discuss the mechanisms of chaos in Hamiltonian systems using the examples of billiards. Billiards appear as natural models in mechanics, optics, acoustics, etc, and form one of the most visual and studied classes of dynamical systems. There are two mechanisms of chaos, which are called dispersing and defocusing. It will be demonstrated that all focusing components of the boundary of chaotic billiards should be absolutely focusing. The absolute focusing is a new notion in geometric optics. In dimensions greater than two the astigmatism puts another restriction on the structure of admissible focusing components. A generic Hamiltonian system is neither chaotic nor integrable, but instead it has a divided phase space where the regions of regular dynamics (KAM islands) coexist with the regions of chaotic dynamics (chaotic seas). Such structure of the phase space has a profound effect on the transport properties of the system. We will present simple visual examples where any number of islands coexist with any number of chaotic seas and show that the transport properties of such systems are nonuniversal.
Friday, April 10 at 4:00 PM
Room L211, Technological Institute
Refreshments are served at 3:30 PM
